Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix

Robust synchronization problem is a key issue in chaotic circuits and nonlinear systems. This paper is concerned with robust synchronization problem of polynomial nonlinear system affected by time-varying uncertainties on topology, i.e., structured uncertain parameters constrained in a bounded-rate polytope. Via partial contraction analysis, novel conditions, both for robust exponential synchronization and for robust asymptotical synchronization, are proposed by using parameter-dependent contraction matrices. In addition, for polynomial nonlinear system, this paper introduces a new class of contraction matrix, i.e., homogeneous parameter-dependent polynomial contraction matrix (HPD-PCM), by which tractable conditions of linear matrix inequalities (LMIs) are provided via affine space parametrizations. Furthermore, the variant rate margin for robust asymptotical synchronization is, for the first time, proposed and investigated via handling generalized eigenvalue problems (GEVPs). A set of representative examples demonstrate the effectiveness of proposed method.